Problem 10 - Elementary Algebra

Question

Add and subtract. $$ -3-7+4 $$

Step-by-Step Solution

Answer

The result of the expression is -6.

Step 1: Identify the Operation

Look at the expression \(-3 - 7 + 4\). Here, you need to perform two operations: subtraction and addition.

Step 2: Perform the Subtraction

Start by performing the subtraction part of the expression. Calculate \(-3 - 7\). This can be thought of as adding two negative numbers:\(-3 + (-7) = -10\).

Step 3: Perform the Addition

Now, take the result from Step 2 and perform the addition. Add \(-10 + 4\), which is the same as moving 4 units up from -10 on a number line. This equals \(-6\).

Key Concepts

Addition and Subtraction

Addition and subtraction are fundamental operations in elementary algebra. They allow us to calculate the total or the difference between numbers. Understanding these operations is vital for solving complex mathematical problems.

To add or subtract, follow these steps:

• Identify the numbers and signs: Look carefully at whether each number is positive or negative.
• Perform the operations step by step: You can tackle them from left to right. First, handle subtraction, then move to addition if needed.
• Watch the order: Always consider the leftmost operation first. It is like reading – move from left to right.

Practice makes perfect, especially with more complex problems involving parentheses or multiple operations.

Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of them. Negative numbers play an important role in mathematics, particularly in operations like subtraction and addition.

For subtraction, consider the following tips:

• Think of the number line: When you subtract a positive number, move to the left. When you subtract a negative number, go to the right.
• Link with addition: Subtracting a negative is essentially adding the positive counterpart of the number.

For example, subtracting a negative number \(- (-3)\) simplifies to \(+3\). Understanding these nuances ensures accurate calculations and helps in developing number sense.

Mathematical Operations

Mathematical operations include addition, subtraction, multiplication, and division. These are the building blocks for solving mathematical expressions and equations.

When dealing with these operations:

• Follow the order of operations: Known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule guides the sequence in which operations should be performed.
• Be aware of the signs: Positive and negative signs can change the outcome of operations, especially when dealing with addition and subtraction.
• Use number lines: Number lines can be a helpful visual aid, particularly for understanding negative numbers and performing basic operations.

By understanding these basic operations and their rules, you can more effectively tackle algebraic expressions, ensuring accuracy in your calculations.